1. Data Mining(中国人民大学) Yang qiang(香港科技大学) Han jia wei(UIUC)
Classification
Han jia wei(UIUC)
Information Network Data Mining
Pei jian（Simon Fraser University）
Uncertainty Data and Model

2. DECISION TREE [Quinlan93]
An internal node represents a test on an attribute.
A branch represents an outcome of the test, e.g., Color=red.
A leaf node represents a class label or class label distribution.
At each node, one attribute is chosen to split training examples into distinct classes as much as possible
A new case is classified by following a matching path to a leaf node.

3. Training Set

4. Example Outlook sunny overcast rain humidity P windy high normal true
false N P N P

5. Building Decision Tree [Q93]
Top-down tree construction
At start, all training examples are at the root.
Partition the examples recursively by choosing one attribute each time.
Bottom-up tree pruning
Remove subtrees or branches, in a bottom-up manner, to improve the estimated accuracy on new cases.

6. Choosing the Splitting Attribute
At each node, available attributes are evaluated on the basis of separating the classes of the training examples. A Goodness function is used for this purpose.
Typical goodness functions:
information gain (ID3/C4.5)
information gain ratio
gini index

7. Which attribute to select?

8. A criterion for attribute selection
Which is the best attribute?
The one which will result in the smallest tree
Heuristic: choose the attribute that produces the “purest” nodes
Popular impurity criterion: information gain
Information gain increases with the average purity of the subsets that an attribute produces
Underlying criterion: Entropy ,Gini, Misclassification error
Strategy: choose attribute that results in greatest information gain
The largest difference between Gini  impurity and entropy is that entropy peaks slower and as a result it tends to penalize mixed sets a little more heavily.  It is more commonly used than Gini impurity but easily swapped out.  

9. Computing information
Information is measured in bits
Given a probability distribution, the info required to predict an event is the distribution’s entropy
Entropy gives the information required in bits (this can involve fractions of bits!)
Formula for computing the entropy:
Suppose a set S has n values: V1, V2, …Vn, where Vi has proportion pi,
E.g., the weather data has 2 values: Play=P and Play=N. Thus, p1=9/14, p2=5/14.
在信息增益中，衡量标准是看特征能够为分类系统带来多少信息，带来的信息越多，该特征越重要。对一个特征而言，系统有它和没它时信息量将发生变化，而前后信息量的差值就是这个特征给系统带来的信息量。所谓信息量，其实就是熵。

10. Example: attribute “Outlook”
“Outlook” = “Sunny”:
“Outlook” = “Overcast”:
“Outlook” = “Rainy”:
Expected information for attribute:
Note: this is
normally not
defined.

11. Computing the information gain
Information gain: information before splitting – information after splitting
Information gain for attributes from weather data:

12. Continuing to split

13. The final decision tree
When all cases have the same class. The leaf node is labeled by this class.
When there is no available attribute. The leaf node is labeled by the majority class.
When the number of cases is less than a specified threshold. The leaf node is labeled by the majority class.
Note: not all leaves need to be pure; sometimes identical instances have different classes
 Splitting stops when data can’t be split any further

14. Highly-branching attributes
Problematic: attributes with a large number of values (extreme case: ID code)
Subsets are more likely to be pure if there is a large number of values
Information gain is biased towards choosing attributes with a large number of values
This may result in overfitting (selection of an attribute that is non-optimal for prediction)
Another problem: fragmentation

15. The gain ratio
Gain ratio: a modification of the information gain that reduces its bias on high-branch attributes
Gain ratio takes number and size of branches into account when choosing an attribute
It corrects the information gain by taking the intrinsic information of a split into account
Also called split ratio
Intrinsic information: entropy of distribution of instances into branches
(i.e. how much info do we need to tell which branch an instance belongs to)

16. Gain Ratio IntrinsicInfo should be
Large when data is evenly spread over all branches
Small when all data belong to one branch
Gain ratio (Quinlan’86) normalizes info gain by IntrinsicInfo:
May choose an attribute just because its intrinsic information is very low
Standard fix:
First, only consider attributes with greater than average information gain
Then, compare them on gain ratio

17. Pruning
Pruning simplifies a decision tree to prevent overfitting to noise in the data
Two main pruning strategies:
Postpruning: takes a fully-grown decision tree and discards unreliable parts
Prepruning: stops growing a branch when information becomes unreliable
Postpruning preferred in practice because of early stopping in prepruning